If a light ray incident on an equilateral prism suffers minimum deviation at an angle 30° , then speed of light in the prism will be

Given, 60° A  for equilateral prism and ${\mathrm{D}}_{\mathrm{m}}={30}^{\circ }$
According to prism formula,
$\begin{array}{l}\mathrm{n}=\frac{\sin \left(\frac{\mathrm{A}+{\mathrm{D}}_{\mathrm{m}}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}\\ \mathrm{n}=\frac{\sin \left(\frac{{60}^{\circ }+{30}^{\circ }}{2}\right)}{\sin \left(\frac{{60}^{\circ }}{2}\right)}=\frac{\sin {45}^{\circ }}{\sin {30}^{\circ }}\text{ or }\mathrm{n}=\sqrt{2}\\ \because \mathrm{n}=\frac{\text{ Speed of light in air }}{\text{ Speed of light in prism }\left(\mathrm{v}\right)}\end{array}$
$\Rightarrow \mathrm{v}=\frac{\mathrm{c}}{\mathrm{n}}=\frac{3\times {10}^8}{\sqrt{2}}=\frac{3}{\sqrt{2}}\times {10}^8\mathrm{m}/\mathrm{s}$